In music, variation is a formal technique where material is altered during repetition; reiteration with changes. Changes may be harmonic, melodic, contrapuntal, rhythmic, and of timbre or orchestration. Variational sections depend upon one type of presentation of material, while developmental sections use many different presentations and combinations of material.
Variation form, or theme and variation, is a musical form where a theme is repeated in altered form or accompanied in a different manner. Passacaglias and chaconnes are forms in with a repeating bass line or ostinato is heard through the entire piece. Fantasia variation is a form which relies on variation but which repeates and incorporates material freely.
History of variations
Works in theme-and-variation form have been written through most of the history of classical music. A favorite form of variations in Renaissance music was divisions, a type in which the basic rhythmic beat is successively divided into faster and faster intervals. The basic principle of beginning with simple variations and moving on to more elaborate ones has always been present in the history of the variation form, since it provides a way of giving an overall shape to a variation set, rather letting it just form an arbitrary sequence.
Two famous variation sets from the Baroque era, both for harpsichord, are George Frideric Handel's "Harmonious Blacksmith" set, and Johann Sebastian Bach's Goldberg Variations, which together with Beethoven's late variations is widely considered to represent the pinnacle of the form.
In the Classical era, Wolfgang Amadeus Mozart wrote a great number of variations, such as the first movement of his Piano Sonata in A, K. 331, or the finale of his Clarinet Quintet. Mozart favored a particular pattern in his variations: the penultimate variation is in slow tempo, often acting as a kind of extra slow movement in a multi-movement work; and the final variation is fast and in bravura style. Joseph Haydn specialized in sets of double variations, in which two related themes, usually minor and major, are presented and then varied in alternation; one example is the slow movement of his Symphony #103, the "Drumroll".
Ludwig van Beethoven wrote many variation sets in his career. Some were independent sets, of which the most substantial are considered to be the "Diabelli" variations, Op. 120. Others form single movements or parts of movements in larger works, such as first movement of the Piano Sonata Op. 26, or the variations in the final movement of the Third Symphony. Variation sets that listeners often consider to be among Beethoven's most profound musical utterances occur in several of his late works, such as slow movement of his string quartet Op. 127, the second movement of his final piano sonata, Op. 111, and the slow movement of the Ninth Symphony.
Franz Schubert wrote five variation sets using his own lieder as themes. A highlight of these is the slow movement of his string quartet "Death and the Maiden" ("Der Tod und das Mädchen", D. 810), an intense set of variations on his somber lied (D. 531) of the same title. Schubert's Piano Quintet in A ("The Trout", D.667) includes a blithe set of variations on his equally blithe "The Trout" ("Die Forelle", D. 550).
In the Romantic era, the variation receded somewhat in importance, but many composers nevertheless created variation sets. A standout was Johannes Brahms, whose Classical tendencies perhaps naturally inclined him to writing variations. Some of Brahms's variation sets rely on themes by older composers, for example the variations for orchestra on a theme (thought in Brahms's time to be) by Haydn and the variations for piano on a theme by Handel.
Variation sets were also composed by 20th century composers, including Arnold Schoenberg (the Variations for Orchestra), Anton Webern (the Variations, Opus 27 for piano and Variations, Opus 30 for orchestra), Paul Hindemith, and Benjamin Britten (including the Young Person's Guide to the Orchestra (Variations and Fugue on a Theme by Purcell) and the Variations on a Theme by Frank Bridge).
Skilled musicians who know a theme well can often improvise variations on it. This was commonplace in the Baroque era, when the da capo aria, particular when in slow tempo, required the performer to be able to improvise a variation during the return of the main material.
Musicians of the Classical era also could improvise variations. A minor work by Beethoven, his Fantasia in G Minor Op. 77, is almost certainly a written transcription of an improvised performance, at the core of which is a series of variations on a short theme. The great number and somewhat stereotyped character of Mozart's stand-alone variation sets for piano suggest that these, too, may be written-down improvisations, or at least were composed in haste.
Improvisation of elaborate variations on a popular theme is one of the core genres of jazz.
- Classical Music Pages: Variation (http://w3.rz-berlin.mpg.de/cmp/g_variation.html)